Modeling typology for sharp/diamond like objects
Final:



You can do this in couple different ways. I'll present you two of them, and both non destructive.

Base mesh:

As a base mesh you'll need to create diamond shape with triangle-like quads (yes, they are ok, and they are still quads).



Mean Crease method:

Select outer/sharp edges and add to them Mean Crease - I've used 0.96 for base of the mesh (square) and 0.8 for the side ones.

After that add Subdivision Surface modifier.

 

Bevel modifier method:

This one is simpler and recommended.

Add Bevel modifier, choose Limit Method > Angle. Set number of Segments and Width. 

Add Subdivision Surface modifier.